Symmetric Gap Research Articles

The Steklov Problem in a Half-Plane: the Dependence of Eigenvalues on a Piecewise-Constant Coefficient

The Steklov problem considered in the paper describes free two-dimensional oscillations of an ideal, incompressible, heavy fluid in a half-plane covered by a rigid dock with two symmetric gaps. Equivalent reduction of the problem to two spectral problems for integral operators allows us to find limits for all eigenfrequencies as the distance between the gaps tends to zero or infinity. For the fundamental eigenfrequency and the corresponding eigenfunction, two terms are found in the asymptotic expansion as the distance tends to infinity. It is proved that all eigenvalues are simple for any distance. Bibliography: 15 titles.

Comprehensive study of CAD models of several coplanar waveguide (CPW) discontinuities

A comprehensive study of CAD models of several coplanar waveguide (CPW) discontinuities is presented. The following discontinuities are studied: CPW short-end, CPW open-end, symmetric CPW series gap, and symmetric short-end coupled CPW. Simple models, that are suitable for CAD purposes, are proposed and validated by comparison to published full-wave results.

An Investigation of the Fields of Bounded Formal Power Series by Means of Theory of Cuts

We consider a class K of real closed fields F, |F|=|G|=ℵ1, where G is a group of Archimedean classes of F, and cofinality of each symmetric gap of F is ℵ1. We will show that this class is exactly a class of all bounded formal power series R〚G,ℵ1〛, where G is a divisible Abelian group, card(G)=ℵ1, under CH. A nonstandard real line *R, which is η1-set belongs to this class; we will also consider a construction R〚G(L,P),ℵ1〛 of fields from this class, where L is a totally ordered set, P is a totally ordered field, G(L,P) is a group of finite words. It will be describes symmetric gaps of such two fields in K, which are not η1-set.

Tunneling spectroscopy ofBi2Sr2CaCu2O8+δ: Eliashberg analysis of the spectral dip feature

Eliashberg strong-coupling theory, extended to a d-wave symmetric gap function, is used to fit quantitatively a published tunneling spectrum of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ near optimal doping. The shape, location, and strength of the high-bias spectral dip feature is adequately reproduced using a single-peak ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ centered at 36.5 meV. ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ also self-consistently determines the measured gap value $\ensuremath{\Delta}=32\mathrm{meV}.$ Possible origins of the bosonic spectrum that give rise to high-${T}_{C}$ superconductivity are discussed.

Soft tissue balancing in total condylar knee arthroplasty

Soft tissue balancing and correct bone cuts are an entity in correcting malalignment in total knee arthroplasty, and cannot be considered isolated. Distinct bony deformations/deviations need enlarged soft tissue management. The extent of resection of the bone stock has to be planned exactly before the operation. Exact soft tissue balancing is necessary to stabilize the corrected knee. Soft tissue balancing has to be done primarily on the side of the contracture by lengthening of the shortened and contracted structures. After balancing the ligaments should have the same tension in extension and flexion together with the same height of the extension and flexion gap. Because of the classic resection of the tibial head, the femoral resection must follow the Insall-Line, that means 3 degrees to 5 degrees outer rotation in relation to the condyles. Only in this way a symmetric flexion gap can be achieved in combination with ligamentous stability in extension and flexion.

Long-term results of posterior cruciate-substituting total knee arthroplasty.

Posterior cruciate ligament-substituting total knee prostheses have been used extensively since the original posterior-stabilized condylar prosthesis was introduced more than 2 decades ago. The key design principle of this prosthesis was the incorporation of a cam and post mechanism on the femoral and tibial components. This mechanism was intended to function as a mechanical substitute for the posterior cruciate ligament, to optimize prosthesis roll back in flexion, and to avoid flexion instability by preventing posterior subluxation. Central to the use of these devices was the surgical technique, which required resection of both cruciate ligaments and creation of symmetric flexion and extension gaps with equal medial and lateral soft tissue tension. Modifications to the original design have been introduced gradually; these include changes to the patellofemoral geometry, and the addition of monoblock and modular metal-backed tibial components. Despite these changes, the key concepts of the prosthesis design and surgical technique have remained constant. The clinical results obtained with the use of these designs have been reported extensively. Long-term results at greater than 10 years continue to duplicate the outstanding early results with prosthesis survivorship exceeding 95% and high levels of patient function.

Sloshing problem in a half-plane covered by a dock with two gaps: monotonicity and asymptotics of eigenvalues

The two-dimensional sloshing problem is considered in a half-plane covered by a rigid dock with two symmetric gaps. It is proved that the antisymmetric (symmetric) sloshing eigenvalues are monotonically decreasing (increasing) functions of spacing between gaps and formulae for their derivatives are obtained.

Knee: Axial instability

The long term results of total knee replacement are among the most successful of any orthopedic procedure; however, certain patterns of failure have been identified including varus-valgus instability and anterior-posterior instability in flexion. While trauma may cause acute ligamentous injury that results in instability, the majority of cases likely result from intraoperative decisions that result in malalignment and inadequate soft tissue balancing. Failure to restore medial-lateral soft tissue balance with symmetric flexion and extension spaces may result in postoperative instability. Techniques to achieve correct soft tissue balancing and symmetric flexion and extension gaps, as well as the management of postoperative instability, are reviewed.

Primary total knee arthroplasty in the valgus knee: Creating a balanced soft tissue envelope

Lateral tissue releases in valgus total knee arthroplasty frequently produce asymmetric flexion-extension gaps and ligamentous instability. This study compared 2 lateral-release sequences and quantified the effects of sequential lateral capsular ligamentous structure release. One knee from 7 paired specimens was released according to a 4-step sequence: posterior cruciate ligament (PCL), ibiotibial tract (IT band), popliteus tendon/lateral collateral ligament (PT/LCL), and biceps femoris tendon. The contralateral knees were released according to a 5-step sequence: PCL, posterolateral capsule, IT band, PT, and LCL. After each release step, flexion and extension gaps were measured and recorded for the medial and lateral aspects. The 5-step sequence produced more symmetric flexion-extension gaps, whereas the absolute magnitudes of correction were lower than with the 4-step sequence. LCL sacrifice in both sequences produced marked lateral flexion-extension gap asymmetry.

Variation of Gaps between an Elastic Body and an Irregular Base under the Action of Concentrated Forces

We study the problem of contact interaction of an elastic half plane with a rigid base containing a smooth hollow under the action of external pressure and concentrated forces. We analyze the processes of appearance and transformation of intercontact gaps in the case where the force approaches the boundary. It is shown that, after the appearance of two symmetric gaps, the evolution of contact passes through three stages as the distance between the force and the boundary decreases. In the first stage, the gaps become smaller and, as a final result, disappear. In the second stage, the bodies are in perfect contact. In the third stage, the contact opens again and the gaps become larger as the force approaches the boundary.

Computing Lippmann Diagrams from Direct Calculation of Mixing Properties of Solid Solutions: Application to the Barite-Celestite System

The Lippmann diagram for the system(Ba, Sr)SO4-H2O was computed at 25 °Cby determining the solid-phase activity coefficientsfrom first principles calculations. Directcalculations of the mixing properties of thebarite-celestite series indicate this solid solutionbehaves as non-ideal and non-regular. At 25 °C,the enthalpy of mixing shows a minimum around 50 mole% SrSO4 due to an ordering tendency. Thefree energy of mixing shows two minima that delimit awide and symmetric miscibility gap (from 2.1 to 97.9 mole% SrSO4) at this temperature. The excessfree energy of mixing requires a Guggenheim expansionseries of 5 terms to be described, where the termswith odd exponents are null as a consequence of thesymmetric distribution of the mixing properties withcomposition. The Lippmann diagram shows a peritecticpoint that corresponds to the composition of an aqueoussolution which is simultaneously at equilibrium withthe two extremes of the miscibility gap. The largedifference between the solubility products of theendmembers involves a strong preferential partitioningof the less soluble endmember towards the solid phase,which explains the extremely Ba-poor composition ofthe aqueous solution (aqueous activity fraction forBa2+ = 0.000446 ) at the peritectic point.

On the entropy devil’s staircase in a family of gap-tent maps

To analyze the trade-off between channel capacity and noise-resistance in designing dynamical systems to pursue the idea of communications with chaos, we perform a measure theoretic analysis the topological entropy function of a ‘gap-tent map’ whose invariant set is an unstable chaotic saddle of the tent map. Our model system, the ‘gap-tent map’ is a family of tent maps with a symmetric gap, which mimics the presence of noise in physical realizations of chaotic systems, and for this model, we can perform many calculations in closed form. We demonstrate that the dependence of the topological entropy on the size of the gap has a structure of the devil’s staircase. By integrating over a fractal measure, we obtain analytical, piece-wise differentiable approximations of this dependence. Applying concepts of the kneading theory we find the position and the values of the entropy for all leading entropy plateaus. Similar properties hold also for the dependence of the fractal dimension of the invariant set and the escape rate.

Subgap conductance features ofYBa2Cu3O7−δedge Josephson junctions

The differential conductance of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ edge junctions with a ${\mathrm{PrBa}}_{2}{\mathrm{Cu}}_{2.9}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}\mathrm{}}$ barrier has been investigated in detail. One striking property of our edge junctions is the existence of a well pronounced, symmetric subharmonic gap structure which is observed in the differential conductance. These features can be explained by multiple Andreev reflections if we assume the existence of a second peak in the density of states. Furthermore, a zero-bias peak in the conductivity was observed in some of the junctions, which may be explained by Andreev bound states at the interface of a d-wave superconductor.

Slow convergence of the Gibbs sampler

AbstractWe consider the Gibbs sampler as a tool for generating an absolutely continuous probability measure ≥ on Rd. When an appropriate irreducibility condition is satisfied, the Gibbs Markov chain (Xn;n ≥ 0) converges in total variation to its target distribution ≥. Sufficient conditions for geometric convergence have been given by various authors. Here we illustrate, by means of simple examples, how slow the convergence can be. In particular, we show that given a sequence of positive numbers decreasing to zero, say (bn;n ≥ 1), one can construct an absolutely continuous probability measure ≥ on Rd which is such that the total variation distance between ≥ and the distribution of Xn, converges to 0 at a rate slower than that of the sequence (bn;n ≥ 1). This can even be done in such a way that ≥ is the uniform distribution over a bounded connected open subset of Rd. Our results extend to hit‐and‐run samplers with direction distributions having supports with symmetric gaps.

Analytical evaluation of the asymptotic impedance matrix of asymmetric gap discontinuities

New analytical formulas have been developed for evaluating the asymptotic impedance matrix of an asymmetric gap by using the integral transform method. Application of the newly derived formulas shows a dramatic improvement of the computation time for evaluating the overall impedance-matrix elements for the symmetric and asymmetric gaps while retaining the accuracy.

V. Mechanism of Superconductivity

A possibility of phonon-mediated interaction as a mechanism of high- T c superconductivity is discussed. Because of different spatial distribution of Bloch wave function for up-spin particle and down-spin particle in the present model, the effective pair interaction which is derived from electron–phonon interaction is shown to have significant momentum- transfer dependence that is quite different from ordinary phonon-mediated interaction. This characteristic of pair interaction together with the geometric feature of Fermi-surface derived in a previous paper III leads to a dx2-y2 symmetric gap state which is consistent with experimental results. Since d-wave state has much smaller Coulomb repulsion term than s-wave state, strong electron-phonon coupling in the present model is expected to cause the occurrence of high-temperature superconductivity. However, in the present model, it is shown that a factor that reduces superconducting transition temperature appear as a result of a fluctuation effect of antiferromagnetic (AF) order of localized Cu spins. The factor λs which should be proportional to AF correlation length λ AF , determines the time scale τs which eliminates the contribution from the retarded effective pair interaction of time argument larger than τs. Existence of length scale λs explains why T c goes to zero as increasing hole carrier to some extent, and why non-magnetic impurity such as Pb reduces T c strongly. λs also explains the finite density of zero-gap states observed in overdoped regime or samples with non-magnetic impurities.

CAD model of a gap in a coplanar waveguide

The partial capacitance approach and conformal mapping techniques are used to evaluate simple closed-form models for parallel and series capacitances of equivalent π-network of a symmetric gap in a CPW. Models are compared with experimental data and full wave analysis. They are useful for a wide range of CPW parameters and frequencies. © 1996 John Wiley & Sons, Inc.

CAD model of a gap in a coplanar waveguide

The partial capacitance approach and conformal mapping techniques are used to evaluate simple closed-form models for parallel and series capacitances of equivalent π-network of a symmetric gap in a CPW. Models are compared with experimental data and full wave analysis. They are useful for a wide range of CPW parameters and frequencies. © 1996 John Wiley & Sons, Inc.

Problems of tunneling spectroscopy at oxide covered Ti

Problems of tunneling spectroscopy are discussed for TiO2, various tips and environments. Calibration measurements on gold surfaces with Au, Ti and W tips in dry nitrogen and air respectively show possible artefacts. Reversible, linear VT- and DT-spectra were obtained only in dry nitrogen. Measurements in air or with oxide covered tips, eg Ti, are ill-defined and suffer from changes in the tunneling system.VT-spectra of oxide covered titanium as a substrate with Au-tips in dry nitrogen strongly depend on the oxide thickness. The inverse system Au (substrate)/Ti-tip gives spectra similar to ultrathin oxide films on titanium with a gold tip. DTS measurements indicate a penetration of the tip into the oxide. The correlation between obtained symmetric gaps and the unsymmetric band gap of the n-type semiconductor TiO2 is questioned. The unexpected influence of the U(t) scan type proves that modifications of TiO2 cannot be excluded even in dry nitrogen. Detected modifications in wet air may be useful, however, for nanotechnology.

Coefficients of multivalent symmetric functions of bounded boundary rotation

In this paper the sharp coefficient estimate problem for the classesCp(β, m) andVp(k,m) of multivalent close-to-convex functions of order β and multivalent functions of bounded boundary rotation of at mostkπ, whose functions are given bym-fold symmetric gap series, have been discussed respectively for β≥1−p/m>0 andk≥2(m/p). Moreover, it is shown that every function inVp(k,m) arep-valent close-to-convex; hencep-valent; ifk<2 (1+m/p).